The standard answer here is that God is constrained by His nature not to overwhelm his Creation. In any situation where two parties are highly unequal in power but desiring relationship, the more powerful party must take extra care.
Imagine, for example, Queen Elizabeth I, being courted by a suitor who would inherently become King of England. Were she to fall in love with a commoner, for example, Bess would never be sure if her would-be suitor had fallen in love with her or her wealth. Indeed, even the man could even doubt himself. Likewise the suitor would be constrained in the risks he might take- for if he really screwed up, she would have the right to take his head!
It is thus an axiom that relationships between unequals must occur in the context in which the more powerful abrogates the privileges of power in order to allow each member the opportunity to pursue the relationship without regard to the power.
Given this understanding, any situation in which God chose to exercise his abity to grant one the ability to feel his infinite joy would be tantamount to the Queen offering the suitor the whole Kkngdom. It is a gift so great that it would inherently re distort the power. It would be too easy to be a bribe, making it impossible for the suitor to distinguish between the gift and the giver.
As such, it must be God's nature to woo, not to whelm. And, God, having designed man to behave a certain way constrains himself to the design he set. While he may have the ability to break his own rule at any time, chooses ala the Law of Non-Contradiction not too, in order to afford His finite creation the chance to comprehend him.
As such, the answer is, could he give infinite joy at any time? Sure. But to do so would violate his nature and his purpose. He wants us to love Him, but will not 'buy us off.' Until we are in perfect relationship with Him, the theory itself inherently overrides the possibility of it being tested.